kinematic modelling of extensional fault-propagation folding

Kinematic modelling of extensional fault-propagation folding

Stuart Hardya,*, Ken McClayb

aBasin and Stratigraphic Studies Group, Department of Earth Sciences, The University of Manchester, Manchester M13 9PL, UKbFault Dynamics Research Group, Department of Geology, Royal Holloway University of London, Egham Hill, Egham, Surrey, TW20 0EX, UK

Received 9 February 1998; accepted 17 March 1999

Abstract

Many studies have shown that in extensional basins discrete faulting at depth is commonly linked to more distributeddeformation, in particular folding, at higher levels. Such extensional fault-propagation folds are particularly common wherethere is a distinct mechanical contrast between faulted basement and sedimentary cover. Outcrop and analogue modelling studies

indicate that such folds form as upward widening zones of distributed deformation (monoclines) above discrete faults at depth.With increasing displacement (strain) the folds are cut by faults as they propagate upwards into the cover. To date, however,there has been little investigation into the kinematics of linked basement faulting and extensional fault-propagation folding.

Here we present a two-dimensional kinematic model of linked basement faulting and fault-propagation folding which is basedupon trishear. The model allows investigation of the in¯uence of shear zone geometry and the rate of fault propagation uponthe style of folds and the strains associated with them. The evolution of linked basement faulting and folding predicted by themodel is compared in detail to that observed in an analogue model. The kinematic model reproduces well many of the features

seen both in the analogue model and reported from outcrop and seismic studies. # 1999 Elsevier Science Ltd. All rightsreserved.

1. Introduction

Extensional fault-propagation folds form abovesteeply dipping normal faults (Fig. 1a and b) typically,though not exclusively, where there is a distinct mech-anical contrast between basement and sedimentarycover or a ductile unit overlies the basement and actsto decouple the basement and overlying sediments (seeWithjack et al., 1990; Stewart et al., 1996; Gawthorpeet al., 1997). They have been recognized from manyareas of the world, e.g. the Rhine Graben (Laubscher,1982), the Gulf of Suez (Gawthorpe et al., 1997) andthe North Sea (Withjack et al., 1988), and havereceived much attention due to the frequent occurrenceof hydrocarbons associated with the folds themselvesand the underlying fault blocks. Evidence from well-exposed folds with preserved growth strata(Gawthorpe et al., 1997) and from analogue (Withjack

et al., 1990) and numerical modelling (Patton andFletcher, 1995) has indicated that extensional fault-propagation folds form as upward widening zones ofdistributed deformation (monoclines) above discretefaults at depth. Field studies indicate that a variety ofmechanisms are responsible for the distributed defor-mation including ductile ¯ow, bedding slip, rigid ro-tation and small extensional and thrust faults (e.g.Gawthorpe et al., 1997). Analogue modelling studieshave shown that with increasing displacement (strain)the overlying fold is cut by the fault as it propagatesupwards into the cover. Where a faulted rigid base-ment is involved in the deformation the folds are oftencalled forced folds (Withjack et al., 1990), while it hasbeen suggested by Schlische (1995) that the drag foldsof some workers are in fact breached extensional fault-propagation folds. While these aspects of extensionalfault-propagation folds are reasonably well understood(e.g. Schlische, 1995; Janecke et al., 1998), the kin-ematics of the linkage between deeper faulting andshallower distributed deformation is not. Here we pre-sent a two-dimensional kinematic model of linked

Journal of Structural Geology 21 (1999) 695±702

0191-8141/99/$ - see front matter # 1999 Elsevier Science Ltd. All rights reserved.

PII: S0191-8141(99 )00072 -3

* Corresponding author.

E-mail address: [email protected] (S. Hardy)

basement faulting and extensional fault-propagationfolding which builds upon an earlier adaptation oftrishear (Hardy and Ford, 1997), and use this modelto investigate the in¯uence of shear zone geometry andthe rate of fault propagation on both the geometry of,and the strain variation within, extensional fault-propagation folds. The predictions of the model arecompared to a laboratory analogue model and ®eldexamples. The model is shown to account well formany of the features seen both in outcrop examplesand analogue modelling studies.

2. Two-dimensional kinematic model

Field and experimental studies (Fig. 1a, b, c) indi-cate that distinct faulting at depth is often expressed atshallower levels by upward widening zones of distribu-ted deformation (generally monoclinal) in which thereis no distinct throughgoing fault. These broadly tri-angular zones of deformation narrow downsection anddie out near the fault tip. As discussed previously withreference to compressional structures (Hardy andFord, 1997), this is very similar geometrically to the

trishear model (Erslev, 1991) where a triangular zoneof distributed deformation (shearing) is attached to afault tip (Fig. 1d) and can be either hanging wall- orfootwall-®xed. Within the shear zone both the magni-tude and direction of the displacement vector vary,with slip tending to zero towards the footwall. Hardyand Ford (1997) used the trishear model in a compres-sional setting to address a more general situation in

pCPKn

Kum

Kuc

Te

Tmp

PKn

1 km

Kum

(a) (b)

(c) (d)

Footwall

Hangingwalltriangularshear zone

fault tip

Fig. 1. (a), (b) Cross-sections from analogue (clay) models illustrating extensional fault-propagation foldsÐhighlighted in gray shading (redrawn

from Withjack et al., 1990), (c) outcrop of a breached fold from the Gulf of Suez (redrawn from Withjack et al., 1990; pCÐPrecambrian,

PKnÐCarboniferous, Upper Cretaceous, KumÐUpper Cretaceous, KucÐUpper Cretaceous, Paleocene, TeÐEocene, TmpÐMiocene, Pliocene,

Holocene), (d) schematic illustration of the kinematic model of fault-propagation folding used in this paperÐsee text for further details.

Basement

Cover

Normal Fault 1.5 km

Fig. 2. Initial con®guration of the models discussed in this paper. A

distinct normal fault at depth is overlain by a 1.5 km thick cover

stratigraphy. No vertical exaggeration.

S. Hardy, K. McClay / Journal of Structural Geology 21 (1999) 695±702696

which the zone of distributed deformation is attachedto a fault tip which propagates up through a sedimen-tary section at a rate which is independent of the sliprate. Fault propagation from a ¯at deÂ collement andgrowth strata were also incorporated into the model.The detailed derivations of the velocity description of

deformation for the trishear model (the kinematics)and its implementation are given in Hardy and Ford(1997).

Here we apply this kinematic model to the problemof extensional fault-propagation folding where thezone of distributed deformation is assumed to be ®xedto a fault tip which originally lies at the basement±cover interface (Fig. 2). Within the basement weassume that there exists initially a discrete faultwhereas in the cover there is no faulting. As slip occurson the basement fault the overlying strata aredeformed within the shear zone. The nature and lo-cation of deformation during fault slip are controlledby two parametersÐthe apical angle of the shear zoneand the fault propagation to slip ratio ( p/s ). The api-cal angle of the shear zone controls how widely defor-mation is distributed above the fault tip, while p/scontrols how rapidly the fault tip (and its associatedzone of deformation) propagates upwards through therock mass. This model is used here to investigate thein¯uence of shear zone geometry and rates of faultpropagation on both the style of, and strain within,extensional fault-propagation folds. The deformationis monitored with respect to the initially ¯at-lying, con-stant-thickness beds and also through the use of in-itially circular strain markers. The detailed modellingmethodology is given in Hardy and Ford (1997).

3. Modelling of extensional fault-propagation foldgeometries

In this section some examples of the structural re-lationships that are produced by the kinematic modelof extensional fault-propagation folding describedabove are presented. In all the models a normal faultcutting basement at 608 will be used together with aninitial unfaulted cover stratigraphy 1.5 km thick (Fig.2). Models were run for a total of 1 Ma using a sliprate of 0.5 m/ka parallel to the fault. In this sectionthe in¯uence of two parameters on the geometries ofthe structures developed will be investigated: the shearzone apex angle and the fault-propagation to slip( p/s ) ratio.

Fig. 3 shows the sequential development of the basicmodel described above using a shear zone apex angleof 408 and p/s of 2.0. This model will be used as thestandard model against which the other models will becompared. The development of the structure withincreasing slip (displacement) is shown after 0.25, 0.50,0.75 and 1.00 Ma. It can be seen that an upward-widening monocline forms above the discrete fault inthe basement with beds showing thinning in anticlinalareas. Through time the limb of the monocline stee-pens with the ®nal dip reaching approximately 258. Asthe fault propagates up-section (at a rate controlled by

(a)

(b)

(c)

(d)

1.5 km

0.25 Ma

0.50 Ma

0.75 Ma

1.00 Ma

Fig. 3. Sequential evolution of a model having a 608 normal fault

with a trishear zone with a 408 apical angle attached to its tip. Slip

parallel to the normal fault is 0.5 m/ka over a total run time of

1 Ma. The fault propagates into the cover stratigraphy at twice the

slip rate. Model is shown after (a) 0.25, (b) 0.50, (c) 0.75 and (d)

1.00 Ma. Both the fault and the position of the triangular shear zone

at each stage of development are indicated. No vertical exaggeration.

S. Hardy, K. McClay / Journal of Structural Geology 21 (1999) 695±702 697

p/s ) it can be seen to cut the overlying fold producinghanging wall-synclines and footwall-anticlines on eitherside of the fault plane. These are remnants of the brea-ched monocline and are not the result of `drag' adja-cent to the fault (cf. Fig. 1c). At the end of the modelrun (1 Ma) only a small part of the monocline remainsuncut by the fault.

In Fig. 4 the ®nal results of the basic modeldescribed above with shear zone apex angles of 208,408 and 608 are shown. All other model parametersare identical to those used in Fig. 3. These resultsshow that with decreasing apical angle of the shear

zone the monocline decreases in wavelength butbecomes steeper. As a result, the deformation withinthe shear zone is more intense and localized, resultingin more thinning of beds. It is clear that as the apicalangle of the shear zone tends to zero deformationtakes place in an increasingly narrow and intense zoneahead of the fault tip. This results in hanging wall-syn-clines and footwall-anticlines that are restricted to anarrow zone immediately adjacent to the fault plane.

In Fig. 5 the e�ects of variations in p/s on the basicmodel are shown. The basic model of Fig. 3 was runwith p/s of 1, 2 and 4; all other parameters wereunchanged. It can be seen that with increasing p/svalues the fault-propagation folds are cut increasinglyearly in their development by the propagating fault.Thus, in the model with a p/s of 4, the fault has cutthrough all of the cover stratigraphy and shows only athroughgoing fault with no active zone of distributeddeformation. This structure therefore has undergone atwo-stage evolutionÐan early stage of coupled faultingand distributed deformation followed by a later stagewhen the fault propagated through the entire coverstratigraphy (and broke the surface) and no zone ofdistributed deformation was present. Precisely this typeof evolution has recently been reported from detailedanalysis of growth strata associated with extensionalfaults in the Gulf of Suez (Gawthorpe et al., 1997).

In Fig. 6 the nature of strains in the hanging walland footwall in the immediate vicinity of the faultplane for the models in Fig. 5 are shown. Initially cir-cular strain markers were included in these model runsto assess the strain. These strain markers initially havea radius of 50 m and thus represent the strain at scaleslarger than typical outcrops. What can be seen is thatwhile in all of the models the width of the monoclineis broadly similar, the nature of the deformationwithin it is quite di�erent. Low p/s values can be seento lead to greater extensional strains in the fold aheadof the fault tip before being cut (e.g. Fig. 6a) leadingto more ductile fold pro®les. In contrast, with higherp/s values (e.g. Fig. 6c) folds undergo a lesser amountof strain before being cut by the propagating fault.

4. Comparison with an analogue model

Here we test the applicability of our model by com-paring it to a well-constrained analogue (clay) modeldescribed in detail by Withjack et al. (1990). We usean analogue model for comparative purposes as it pro-vides us with a temporal picture of the evolution of afault-propagation foldÐa feature rarely observable innatural examples except when excellent growth strataare preserved. The analogue model is a single-layerclay model above a 758 normal fault. The developmentof the structure is shown after 1, 2 and 3 cm of displa-

(b)

(c)

1.5 km

apical angle= 20°

apical angle= 40°

apical angle= 60°

(a)

Fig. 4. Model results illustrating the e�ect of di�erent apical angles

of the shear zone on fold geometries. Apical angles of (a) 208, (b)408 and (c) 608. Total run time is 1 Ma. All other model parameters

are as in Fig. 3.


cement on the normal fault (Fig. 7a). It can be seenthat a broad upward-widening zone of distributed de-formation develops above the basement fault. Withinthis zone the primary deformation mechanisms arefolding and minor faulting, with both normal faultsand high angle reverse faults developed. With increas-ing displacement the beds above the fault steepenbefore being cut by the fault. The fault propagates andlinks upwards such that after 3 cm of displacement thefold is cut by a throughgoing fault which terminatesthe development of the fold.

The well-constrained nature of this experiment

allows the calibration of our kinematic model. Fromthe published data we observe that an apical angle of808 for the trishear zone approximates well the geome-try of the zone of distributed deformation. Thereforethere remains only one other parameter to be esti-matedÐthe propagation to slip ratio, which, fromqualitative inspection (Fig. 7a), can be seen to be inthe range from 1.0 to 2.0. It was found that the best ®tmodel required a p/s ratio of 1.5. This model and the

(a)

750 m

p/s = 1

(b) p/s = 2

(c) p/s = 4

Fig. 6. Distribution and nature of strain in the fault-propagation

folds of Fig. 5 illustrated by strain markers. All strain markers were

initially circular and had a radius of 50 m.

(a)

(b)

(c)

1.5 km

p/s = 1

p/s = 2

p/s = 4

Fig. 5. Model results illustrating the e�ect of fault propagation to

slip ( p/s ) on fold geometries. Results for p/s ratios of (a) 1.0, (b) 2.0

and (c) 4.0. Total run time is 1 Ma. All other model parameters are

as in Fig. 3.


analogue results at equivalent stages of developmentare shown in Fig. 7(a and b). The close match betweenthe observed and simulated evolution of the structureis remarkable. Many of the details of the structure areaccurately reproduced. In particular, the evolution ofthe monocline and the paired hanging wall-synclinesand footwall-anticlines that develop adjacent to the

fault are very similar to those seen in the analoguemodel. In addition, the spatial distribution of foldingin both the hanging wall and footwall are reproducedwell. Clearly the model does not reproduce the small-scale faulting observed in the clay but the close matchbetween the simulation and the results of Withjack etal. (1990) is very encouraging.

0 cm

1 cm

2 cm

3 cm

(a) (b)

Fig. 7. Comparison of clay analogue modelling results of Withjack et al. (1990) to a model simulation. (a) Analogue model shown after 1, 2 and

3 cm displacement on 758 normal fault. (b) Kinematic model with an apical angle of 808 and a p/s of 1.5 shown at equivalent stages of evolution.


5. Discussion

The model presented here does not attempt to repro-duce in detail the outcrop scale features seen in exten-sional fault-propagation folds. However, it doesattempt to predict the broad-scale features and basiccharacteristics of distributed deformation developedabove discrete faults at depth. At this scale, it repro-duces well many of the features seen both in analoguemodels and reported from outcrop and seismic studies(Withjack et al., 1990; Stewart et al., 1996; Gawthorpeet al., 1997). In particular, the model successfullyreproduces an upward-widening monocline (fault-propagation fold) linked to a discrete fault at depth.In addition, the model produces hanging wall-synclinesand footwall-anticlines adjacent to fault planes thatrepresent breached monoclines rather than dragagainst the fault plane (cf. Fig. 1c). Field studies indi-cate that the deformation predicted by the kinematicmodel is accommodated at the outcrop scale by a var-iety of mechanisms including ductile ¯ow, beddingslip, rigid rotation and small extensional and thrustfaults. While the model does not predict these features,it does predict the spatial variation of strain within aforced fold and the in¯uence of shear zone geometryand fault propagation rate upon both fold style andstrain intensity.

While our initial modelling of the analogue model ofWithjack et al. (1990) has proved successful, a morerigorous approach to such modelling is needed toquantitatively assess the goodness of ®t between thenumerical and analogue models. Allmendinger (1998)has recently published an inverse trishear algorithmwhich allows much more objective calibration of bothapical angle and p/s for just such purposes.

Modelling the mechanical controls on the nature ofthe shear zone, in particular its width, is beyond thescope of this paper. However, Withjack et al. (1990)reported that in their modelling experiments dip of thebasement fault exerted a strong control on the widthof the zone of distributed deformation, with steeperfaults producing narrower zones of deformation. Inthe kinematic model used here, the fault bisects theapical angle of the shear zone, whilst in experimentalresults this is only approximately the case (cf. Fig. 1aand b). The relationship between the shear zone orien-tation and fault dip, together with p/s of the fault,may depend on factors such as the strength of thecover stratigraphy, strain rate, etc. The precise linkagebetween these mechanical factors and our kinematicmodel remain to be further investigated.

In many ways the two-dimensional models presentedhere can also be thought of as representing di�erentstages in the along-strike evolution of a laterally pro-pagating normal fault. Recent authors have noted thatdiscrete (surface-breaking) normal faults often die out

along strike into monoclines (Gawthorpe et al., 1997).We suggest that the temporal evolution of our two-dimensional cross-sections could also represent a snap-shot in the along-strike development of a propagatingnormal fault. This has important implications for boththe nature and amount of accommodation space devel-oped in the hanging wall of a normal fault. Finally, inthis short paper we have concentrated upon the struc-tures seen in strata laid down before deformationbegan. Growth strata, when present (e.g. Gawthorpeet al., 1997), allow further constraints to be placedupon the evolution of extensional fault-propagationfolds. The addition of growth strata to the kinematicmodel described herein is a straightforward task and isthe subject of ongoing work.

6. Conclusions

A two-dimensional kinematic model of extensionalfault-propagation folding, based upon trishear, hasbeen presented in this paper. The model links distribu-ted deformation (in a triangular shear zone) ahead ofa propagating fault tip to discrete faulting at depth.Key parameters of the model are the apical angle ofthe shear zone and the fault-propagation to slip ( p/s )ratio. The kinematic model reproduces well many ofthe features seen both in analogue models andreported from outcrop and seismic studies (Withjack etal., 1990; Stewart et al., 1996; Gawthorpe et al., 1997).In particular the model successfully reproduces anupward-widening monocline (fault-propagation fold)linked to a discrete fault at depth. In addition, themodel predicts hanging wall-synclines and footwall-anticlines adjacent to the fault plane which represent abreached monocline rather than drag against the faultplane. The model also successfully reproduces thedetailed evolution of a clay analogue modelling exper-iment.

Acknowledgements

This short paper has bene®ted greatly from discus-sions with many colleagues, in particular Mary Ford,Rob Gawthorpe, Ian Sharp, John Suppe, GreggErickson and Tim Dooley. Reviews by Eric Erslev andMark Rowan have greatly improved the scope andpresentation of the manuscript. A special thanks mustgo to Rick Allmendinger for his open exchange ofideas and code on trishear kinematics. The ®rst authorstarted this work while part of the Princeton StructureGroup whose support is gratefully acknowledged.


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kinematic modelling of extensional fault-propagation folding

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